Strategies

Boss Run

From McDuff's Workshop bonfire in the Lost Bastille, go past the Undead Jailer on top of the stairs and kill the three Dogs: two in the front, one to the right. Stand where the dog to the right was. Peer down and in the building nearby there will be a locked door.

This door can be opened from the other side and serve as a shortcut to the boss if you can land on it from above.

Next time after the Ruin Sentinels mercilessly slaughter you, all you need to do is run past the dogs to the right hand side dog and jump from one building to another and then go up the stairs.

General

You start off the fight by dropping onto a small platform. Ruin Sentinel Yahim attacks as soon as you enter, but he is alone. Dropping down from the platform or killing Yahim triggers the aggression of the two other Sentinels.
After killing Yahim, the second Sentinel should jump up on the platform shortly thereafter, allowing you to solo it for a bit before the third one jumps up. When both make it up there, it's time to leave the platform and fight on the floor below.

When fighting in the arena below, keep both Sentinels in sight. Counterattack when both Sentinels are recovering from their attack.

You'll want to learn their telegraphs, these will let you dodge or block effectively. Stick close to one of the other two and try to bait out their two handed slam, leaps, or one handed combo. These have about two seconds of recovery animation that you can exploit. Otherwise just kite them away from each other, keep them in your vision

If you have a summon either try to keep the two remaining Sentinels busy at opposite ends of the arena or focus both of your attacks on one to try and kill it quickly. One on it's own is not particularly challenging, just keep calm and watch for the telegraphs.

Tank and Caster

Get the Redeye Ring so that the Sentinels will be paying full attention to you. Use a shield that has good physical resistance and stability, a greatshield of any kind is the best choice.

Summon Pilgrim Bellclaire for the fight. She deals nice amount of damage, especially if her AI decides to spam Soul Spear.

You should be able to block all attacks with no problem. Lower your shield every now and then to improve stamina regeneration.

At the start of the fight lock Yahim to a corner so he will be focusing all of his attacks on you, leaving his back very vulnerable for Pilgrim Bellclaire to unload her powerful spells. When the second Ruin Sentinel jumps over to the ledge, lock on to her and tank her blows. Make sure Bellclaire is safe from harm. When the third Ruin Sentinel joins the fun, drop down and one of them will follow you. Just keep tanking the one that does while Bellclaire finishes the other one. After Bellclaire finished her opponent, she'll come over and help you kill the last Ruin Sentinel.

Notes

The fight against Yahim, Alessia and Ricce in The Lost Bastille is optional. It is skipped by using the Antiquated Key to take the cage elevator up to Straid and the bridge to Sinner's Rise, but this method does not allow access to the Servants' Quarters bonfire or Belfry Luna.

In Dark Souls II, whilst in Drangleic Castle, the Ruin Sentinels will not respawn at Bonfire Intensity 2 or above. This was fixed in Dark Souls II: Scholar of the First Sin.